You can run queries on std::set (std::set::find()) in parallel, but additions and removals must be serialized. To my knowledge any set data structure will have the same constraints, or it will have other limitations, such as occasionally returning the wrong answer.
Are you having performance problems? Although not the fastest data structure, std::set is reasonably quick for most scenarios. If you're having performance problems you should make sure you're not doing something silly.
I know next to nothing about OpenMP, but I do not believe so.
The reason is fairly mundane, actually: a set has a single main purpose:
• verify that an element is a member of the set
This cannot be done in any multithreaded way without synchronizing multiple threads, and the effort to do that typically outweighs what it takes to perform a lookup.
If you are dealing with literally billions of elements, then you are dealing with specialized memory handling already, and separating such a giant set into multiple objects is natural — at which point using multiple threads/processors/servers to check membership is not anything odd.
There is no reason that std::set should need to handle multiple threads.
You can do it, actually, by playing with the set’s allocator. Whether this is worth the effort is not something I can answer.
this may be me not knowing what you want to do, but the KISS answer could be to shove your data into TWO (or more) sets and group them together in a class that does the MP stuff by using the built-in tools in parallel on each set and combining the result at the class level.
The correct choice of any data structure requires rather thorough knowledge of the actions required.
For example, any binary tree approach (typical of set) is chosen specifically for quick, frequent insertions and deletions. This is opposed to a sorted vector (or array), because insertion and removal of sorted information is not efficient, but searching is usually much faster, making it more suited in situations where searching is frequent but insertion and deletion almost never happens.
So, with your limited description, no one is in a good position to advise beyond what can be done for a binary tree structure.
Since the tree structure is balanced, the balancing algorithms quash the hope of threading insertion and deletion (thus, no parallel operation).
If you can be more specific about your application usage pattern, there may be more to offer.